A note on the accuracy of PAC-likelihood inference with microsatellite data

Stephens and Donnelly have introduced a simple yet powerful importance sampling scheme for computing the likelihood in population genetic models. Fundamental to the method is an approximation to the conditional probability of the allelic type of an additional gene, given those currently in the sample. As noted by Li and Stephens, the product of these conditional probabilities for a sequence of draws that gives the frequency of allelic types in a sample is an approximation to the likelihood, and can be used directly in inference. The aim of this note is to demonstrate the high level of accuracy of "product of approximate conditionals" (PAC) likelihood when used with microsatellite data. Results obtained on simulated microsatellite data show that this strategy leads to a negligible bias over a wide range of the scaled mutation parameter theta. Furthermore, the sampling variance of likelihood estimates as well as the computation time are lower than that obtained with importance sampling on the whole range of theta. It follows that this approach represents an efficient substitute to IS algorithms in computer intensive (e.g. MCMC) inference methods in population genetics. (c) 2006 Elsevier Inc. All rights reserved.

Phylogenetic relationships within the moss family Bryaceae based on chloroplast DNA evidence

The Bryaceae are a large cosmopolitan family of mosses containing genera of considerable taxonomic difficulty. Phylogenetic relationships within the family were inferred using data from chloroplast DNA sequences (rps4 and trnL-trnF region). Parsimony and maximum likelihood optimality criteria, and Bayesian phylogenetic inference procedures were employed to reconstruct relationships. The genera Bryum and Brachymenium are not monophyletic groups. A clade comprising Plagiobryum, Acidodontium, Mielichhoferia macrocarpa, Bryum sects. Bryum, Apalodictyon, Limbata, Leucodontium, Caespiticia, Capillaria (in part: sect. Capillaria), and Brachymenium sect. Dicranobryum, is well supported in all analyses and represents a major lineage within the family. Section Dicranobryum of Brachymenium is more closely related to section Bryum than to the other sections of Brachymenium, as are Mielichhoferia macrocarpa and M. himalayana. Species of Acidodontium form a clade with Anomobryum julaceum. The grouping of species with a rosulate gametophytic growth form suggests the presence of a 'rosulate' clade similar in circumscription to the genus Rosulabryum. Mielichhoferia macrocarpa and M. himalayana are transferred to Bryum as B. porsildii and B. caucasicum, respectively.

Likelihood-free estimation of model evidence

Statistical methods of inference typically require the likelihood function to be computable in a reasonable amount of time. The class of “likelihood-free” methods termed Approximate Bayesian Computation (ABC) is able to eliminate this requirement, replacing the evaluation of the likelihood with simulation from it. Likelihood-free methods have gained in efficiency and popularity in the past few years, following their integration with Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) in order to better explore the parameter space. They have been applied primarily to estimating the parameters of a given model, but can also be used to compare models. Here we present novel likelihood-free approaches to model comparison, based upon the independent estimation of the evidence of each model under study. Key advantages of these approaches over previous techniques are that they allow the exploitation of MCMC or SMC algorithms for exploring the parameter space, and that they do not require a sampler able to mix between models. We validate the proposed methods using a simple exponential family problem before providing a realistic problem from human population genetics: the comparison of different demographic models based upon genetic data from the Y chromosome.

Online bayesian inference in some time-frequency representations of non-stationary processes

The use of Bayesian inference in the inference of time-frequency representations has, thus far, been limited to offline analysis of signals, using a smoothing spline based model of the time-frequency plane. In this paper we introduce a new framework that allows the routine use of Bayesian inference for online estimation of the time-varying spectral density of a locally stationary Gaussian process. The core of our approach is the use of a likelihood inspired by a local Whittle approximation. This choice, along with the use of a recursive algorithm for non-parametric estimation of the local spectral density, permits the use of a particle filter for estimating the time-varying spectral density online. We provide demonstrations of the algorithm through tracking chirps and the analysis of musical data.

Improved likelihood inference for the shape parameter in Weibull regression

We obtain adjustments to the profile likelihood function in Weibull regression models with and without censoring. Specifically, we consider two different modified profile likelihoods: (i) the one proposed by Cox and Reid [Cox, D.R. and Reid, N., 1987, Parameter orthogonality and approximate conditional inference. Journal of the Royal Statistical Society B, 49, 1-39.], and (ii) an approximation to the one proposed by Barndorff-Nielsen [Barndorff-Nielsen, O.E., 1983, On a formula for the distribution of the maximum likelihood estimator. Biometrika, 70, 343-365.], the approximation having been obtained using the results by Fraser and Reid [Fraser, D.A.S. and Reid, N., 1995, Ancillaries and third-order significance. Utilitas Mathematica, 47, 33-53.] and by Fraser et al. [Fraser, D.A.S., Reid, N. and Wu, J., 1999, A simple formula for tail probabilities for frequentist and Bayesian inference. Biometrika, 86, 655-661.]. We focus on point estimation and likelihood ratio tests on the shape parameter in the class of Weibull regression models. We derive some distributional properties of the different maximum likelihood estimators and likelihood ratio tests. The numerical evidence presented in the paper favors the approximation to Barndorff-Nielsen`s adjustment.

Bimodal extension based on the skew-normal distribution with application to pollen data

This paper considers an extension to the skew-normal model through the inclusion of an additional parameter which can lead to both uni- and bi-modal distributions. The paper presents various basic properties of this family of distributions and provides a stochastic representation which is useful for obtaining theoretical properties and to simulate from the distribution. Moreover, the singularity of the Fisher information matrix is investigated and maximum likelihood estimation for a random sample with no covariates is considered. The main motivation is thus to avoid using mixtures in fitting bimodal data as these are well known to be complicated to deal with, particularly because of identifiability problems. Data-based illustrations show that such model can be useful. Copyright (C) 2009 John Wiley & Sons, Ltd.

Bayesian inference for a skew-normal IRT model under the centred parameterization

Item response theory (IRT) comprises a set of statistical models which are useful in many fields, especially when there is interest in studying latent variables. These latent variables are directly considered in the Item Response Models (IRM) and they are usually called latent traits. A usual assumption for parameter estimation of the IRM, considering one group of examinees, is to assume that the latent traits are random variables which follow a standard normal distribution. However, many works suggest that this assumption does not apply in many cases. Furthermore, when this assumption does not hold, the parameter estimates tend to be biased and misleading inference can be obtained. Therefore, it is important to model the distribution of the latent traits properly. In this paper we present an alternative latent traits modeling based on the so-called skew-normal distribution; see Genton (2004). We used the centred parameterization, which was proposed by Azzalini (1985). This approach ensures the model identifiability as pointed out by Azevedo et al. (2009b). Also, a Metropolis Hastings within Gibbs sampling (MHWGS) algorithm was built for parameter estimation by using an augmented data approach. A simulation study was performed in order to assess the parameter recovery in the proposed model and the estimation method, and the effect of the asymmetry level of the latent traits distribution on the parameter estimation. Also, a comparison of our approach with other estimation methods (which consider the assumption of symmetric normality for the latent traits distribution) was considered. The results indicated that our proposed algorithm recovers properly all parameters. Specifically, the greater the asymmetry level, the better the performance of our approach compared with other approaches, mainly in the presence of small sample sizes (number of examinees). Furthermore, we analyzed a real data set which presents indication of asymmetry concerning the latent traits distribution. The results obtained by using our approach confirmed the presence of strong negative asymmetry of the latent traits distribution. (C) 2010 Elsevier B.V. All rights reserved.

Improved likelihood inference in Birnbaum-Saunders regressions

The Birnbaum-Saunders regression model is commonly used in reliability studies. We address the issue of performing inference in this class of models when the number of observations is small. Our simulation results suggest that the likelihood ratio test tends to be liberal when the sample size is small. We obtain a correction factor which reduces the size distortion of the test. Also, we consider a parametric bootstrap scheme to obtain improved critical values and improved p-values for the likelihood ratio test. The numerical results show that the modified tests are more reliable in finite samples than the usual likelihood ratio test. We also present an empirical application. (C) 2009 Elsevier B.V. All rights reserved.

Likelihood ratio tests for variance components in linear mixed models

Although the asymptotic distributions of the likelihood ratio for testing hypotheses of null variance components in linear mixed models derived by Stram and Lee [1994. Variance components testing in longitudinal mixed effects model. Biometrics 50, 1171-1177] are valid, their proof is based on the work of Self and Liang [1987. Asymptotic properties of maximum likelihood estimators and likelihood tests under nonstandard conditions. J. Amer. Statist. Assoc. 82, 605-610] which requires identically distributed random variables, an assumption not always valid in longitudinal data problems. We use the less restrictive results of Vu and Zhou [1997. Generalization of likelihood ratio tests under nonstandard conditions. Ann. Statist. 25, 897-916] to prove that the proposed mixture of chi-squared distributions is the actual asymptotic distribution of such likelihood ratios used as test statistics for null variance components in models with one or two random effects. We also consider a limited simulation study to evaluate the appropriateness of the asymptotic distribution of such likelihood ratios in moderately sized samples. (C) 2008 Elsevier B.V. All rights reserved.

A fast and robust statistical test based on likelihood ratio with Bartlett correction to identify Granger causality between gene sets

We propose a likelihood ratio test ( LRT) with Bartlett correction in order to identify Granger causality between sets of time series gene expression data. The performance of the proposed test is compared to a previously published bootstrapbased approach. LRT is shown to be significantly faster and statistically powerful even within non- Normal distributions. An R package named gGranger containing an implementation for both Granger causality identification tests is also provided.

Phylogenetic analysis of the order Pleuronectiformes (Teleostei) based on sequences of 12S and 16S mitochondrial genes

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Phylogeny of leafcutter ants in the genus Atta Fabricius (Formicidae: Attini) based on mitochondrial and nuclear DNA sequences

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Ovarian follicle diameter at timed insemination and estrous response influence likelihood of ovulation and pregnancy after estrous synchronization with progesterone or progestin-based protocols in suckled Bos indicus cows

The objectives of the present study were to evaluate factors associated with estrous synchronization responses and pregnancy per insemination (P/AI) in Bos indicus beef cows submitted to progesterone-based fixed-time artificial insemination (FTAI) protocols. A total of 2388 cows (1869 Nellore and 519 crossbred Nellore x Angus) from 10 commercial farms were evaluated to determine the relationships among breed, body condition score (BCS) on the first day of the FTAI protocol, the occurrence of estrus between progesterone device removal and FTAI and diameter of largest ovarian follicle (LF) at FTAI on estrous synchronization responses and P/AI. Cows (n=412 primiparous; 1976 multiparous) received an intravaginal device containing progesterone or an ear implant containing norgestomet (a progestin), and an injection of estradiol at the beginning of the estrous synchronization protocol. Body condition was scored using a 1-5 scale on the first day of the FTAI protocol and at 30-60 days postpartum. Females received 300IU of equine chorionic gonadotropin (eCG) and PGF(2 alpha) on the day the progesterone device/implant was removed and were inseminated 48-60h later. At insemination, cows (n=2388) were submitted to an ultrasonographic exam to determine the diameter of the LF. Follicles were classified into four categories based on mean and standard deviation (SD) of the LF (LF1 = two SD below the mean; LF2 = mean minus one SD; LF3 = mean plus one SD; LF4 = two SD above the mean). Ovulation rate was determined in a subset of cows (n=813) by three consecutive ultrasonographic exams: (1) at time of progesterone device/implant removal, (2) at time of FTAI and (3) 48 h after FTAI. Ovulation was defined as the disappearance of a large follicle (>= 8.0 mm) that was previously recorded. Estrus was determined in a subset of the cows (n = 445) by the activation of a detection of estrous patch placed on the tail head on the day of progesterone device/implant removal. Pregnancy was diagnosed 30 days after FTAI. Pregnancy was influenced (P = 0.001) by follicle diameter [LF1 = 27.5% (81/295), LF2 = 46.6% (328/705), LF3 = 57.9% (647/1118), LF4 = 63.3% (171/270)] and the occurrence of estrus [estrus = 67.7% (174/257) and no estrus = 36.2% (68/188)]. Follicle diameter at FTAI influenced ovulation rate [LF1 = 42.5% (34/80), LF2 = 73.9% (161/218), LF3 = 95.8% (407/425), LF4 = 97.8% (88/90)], the occurrence of estrus [LF1 = 54.8% (51/93), LF2 = 33.6% (43/128), LF3 = 68.9% (126/183), LF4 = 90.2% (37/41)] and P/AI among cows that had ovulations [LF1 =32.4% (11/34), LF2 = 50.3% (81/161), LF3 = 60.0% (244/407), LF4 = 68.2% (60/88)]. Improving estrous responses between progesterone device withdrawal and FTAI and increasing the diameter of the LF at FTAI may be important aspects to achieve improved estrous synchronization responses and P/AI following progesterone/progestin and estradiol based FTAI protocols in suckled Bos indicus cows. (C) 2010 Elsevier B.V. All rights reserved.